Kinoform matched filter method

ABSTRACT

A method of optical filtering in which a phase object is constructed in accordance with the desired matched filter operator and during the filtering operation incoherent light is used. This type of incoherent filtering method is applicable to any filter operator having only nonnegative portions.

United States Patent Lohmann [4 1 Jan. 25, 1972 i 41 KINOFORM MATCHEDFILTER 1 References METHOD OTHER PUBLICATIONS I 721 Lohmann, La 10113,Calif Lohmann, Applied Optics, Vol. 7 No. 3, March 1968 pp. 561- [73]Assignee: International Business Machines Corpora- 563 on, Armonk, NY.Lesem et aL, IBM Jour. of Research &. Development, Vol. 13,

No. 2, March, 1969,pp. 150- 155 [22] Filed: Nov. 26, 1969 [21] APPLNM880,258 Prir nary Examiaer-David Schonberg Assistant ExammerRonald J.Stern Attorney-Hanifin and Jancin and John L. Jackson 52 us. Cl..350/l62 SF, 235/181 [57] ABSTRACT f Cl 8 9/00,G02b 27/38 A method ofoptical filtering in which a phase object is con- [58) Field of Search....350/3.5, 162 SF; 178/68;

structed in accordance with the desired matched filter operator andduring the filtering operationincoherent light is used. This type ofincoherent filtering method is applicable to any filter operator havingonly nonnegative portions.

5 Claims, 4 Drawing Figures VIRTUAL ORDER I s 7 a 2;; HF CENTRAL ORDERREAL F IRST ORDER WAGE FIG- 3 FIGA BY W'/(%6%/WQ ATTORNEYCROSS-REFERENCES TO RELATED APPLICATIONS The Kinoform:-Method ofManufacturing Wave Shaping Devices, invented by P. M. Hirsch, J. A.Jordan, Jr., and L. B. Lesem, filed Nov. 25, 1968, Ser. No. 778,585, andassigned to the assignee of this application.

Discrete Aperture Method of Making Synthetic Kinoforms and Holograms,"invented by P. M. Hirsch, J. A. Jordan, Jr., and L. B. Lesem, filed Jan.29, 1969, Ser. No. 794,977, and assigned to the assignee of thisapplication.

A Method for Figuring Lenses, invented by P. M. Hirsch, J. A. Jordan,Jr., and L. B. Lesem, filed Apr. 4, 1969, Ser. No. 813,651, (nowabandoned) and assigned to the assignee of this application.

Computer Generated Filtering Method, invented by P. M. Hirsch, J. A.Jordan, Jr., and L. B. Lesem, filed Nov. 26, 1969 Ser. No. 880,260assigned to the assignee of this application.

BACKGROUND OF THE INVENTION 1. Field of the Invention This inventionrelates to optical information processing and filtering in general, andmore particularly, to computergenerated optical filters for use in anincoherent filtering system.

2. Description of the Prior Art Optical information processing is arelatively new science of image processing using stops and diffractionpatterns. Many mathematical procedures such as multiplication,correlation, etc., are possible using holographic diffraction patternsin a coherent optical system. Correlation can also be achieved inincoherent systems. These operations, together with others such asinverse filtering can be accomplished using computergenerated orsynthetic holographic filters in the coherent optical system. Oneholographic filtering system is described in Applied Optics, Vol. 7, No.3, Mar. 1968 at page 561.

An excellent text treatment is also presented in Introduction to FourierOptics," McGraw-Hill, by Joseph W. Goodman, Chapter 7Spatial Filteringand Optical Information Processing.

The usual holographic optical filtering practice makes use of a laser asa coherent light source, several complicated optical elements, theholographic diffraction pattern, and a detection scheme. Inherent inholographic diffraction patterns are two or more diffraction orders.These may be separated angularly in a two-beam hologram. If they are notseparated, the desired diffraction order is obscured by the undesiredorders. If they are separated, the desired order is diffracted away fromthe optical axis of the laser at the expense of bandwidth. Severalproblems attend the use of conventional optical information processingsystems. These include inefficient utilization of the available lightwhich results from the fact that very little of the light from theobject to be filtered is diffracted by the hologram into the desiredorder. Also, the requirement that orders be separated limits the size ofthe image, which in turn limits the size and/or resolution of the objectto be filtered. Additionally, such systems are usually costly andcomplex and due to the extreme rigidity requirements of coherent imagingsystems, require an optical bench. It is also well known that noiseproblems are also present in any coherent system. Noise may arise fromdust and speckling or diffraction.

Finally, the applications available to coherent filtering systems areseverely limited in that due to the requirement of coherent illuminationreal-time" processing is virtually impossible. That is, if coherentsystems are used, the image must be illuminated coherently. Data, whichmight be in electronic form, for example, must be converted anddisplayed in such a way that a photographic transparency can be made andthis transparency illuminated. This step precludes real-time dataprocessing.

Almost all of the problems associated with coherent, holographic opticalprocessing systems can be eliminated if kinoforms are used. If kinoformsare used in incoherent systems, matched filtering or correlation may beaccomplished.

The kinoform process is described in US. Pat. application Ser. No.778,525, entitled The Kinoform: Method of Manufacturing Wave ShapingDevices," by L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr. andassigned to the same assignee as the present application. In addition,the kinoform process was described in a paper presented to the OpticalSociety of -America Meeting on Mar. 13, 1969 and this paper is publishedin Vol. 13, No. 2 of the IBM Journal of Research and Development, pageet seq.

The kinoform is a wave front reconstruction device which,

like the hologram, provides the display of a three-dimensional image. Incontrast to the hologram, however, the illuminated kinoform yields asingle diffraction order and ideally, all the incident light is used toreconstruct the one image. All the spatial frequency content orbandwidth of the device is available for the single image. 7

A kinofonn operates only on the phase of an incident wave front, beingbased on the assumption that only the phase information in a scatteredwave front is required for the construction of an image of thescattering object. The amplitude of the wave front in the kinoform planeis assumed constant as is approximately true for any diffuselyscattering object in the far field. The kinoform may therefore bethought of as a complex lens which transforms the known wave frontincident upon it into the wave front required to form the desired image.Although it was first conceived as an optical focusing element, thekinoform can be used to transform the wave front of any physicalwaveform; e.g., ultrasound or microwaves.

SUMMARY OF THE INVENTION Briefly, a matched filtering operator to beimplemented is mathematically defined. The filter may, for instance, bethat which has as its impulse response function the intensitydistribution of an object to be matched.

In the present invention in the preferred embodiment, the matrix ofnonnegative values representing the filter is processed, and the phaserequired for a kinoformic representation of this matrix calculated andplotted. The plot is then photoreduced and bleached to provide thekinoform filter. The phase calculation, plotting and bleaching are asdescribed in the aforementioned patent application, Ser. No. 778,525.

During actual filtering the object to be filtered such as a transparencyhaving letters thereon is illuminated with incoherent light whichpreferably is color filtered and diffused. The light scattered by theobject then passes through the filter and the resultant filtered image,imaged by means of a lens.

Other alternate embodiments including one in which the incoherentlyilluminated object to be filtered is scanned through the filter anddisplayed on a cathode-ray tube such that realtime processing isaccomplished, are also provided.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an illustration of a typicalholographic coherent information processing system;

FIG. 2 is an illustration of one embodiment of the subject novelincoherent kinoform information processing system;

FIG. 3 is a photograph of an unfiltered letter B;

FIG. 4 is a photograph of the correlation between the unfiltered letterB shown in FIG. 3 and a kinoform matched filter for the letter B.

DETAILED DESCRIPTION OF THE DRAWINGS To aid in an appreciation andunderstanding of the subject novel technique, refer first to FIG. 1,where there is an illustration of a coherent optical processing system,using holographic members. While this system is described in detail inthe aforementioned Applied Optics reference and Goodman text, a briefdescription will be given to aid in an appreciation of the presentincoherent filtering system. In FIG. 1, a light source 1 such as a laserprovides a coherent, monochromatic wave front which is shaped into aplane or spherical wave front by an objective lens 2, spatial filter 3and collimating lens 4. The wave front 5 illuminates the object 6 whichcontains data which is to be filtered; Le, a convolutional operation isto be carried out on the one-, two-, or three-dimensional data. Asillustrated in FIG. 1, the data is carried on a transparency such that acoherent wave front is scattered from it. The wave front 7 illuminatesthe holographic member 8. Most of the light is transmitted in thecentral diffraction order, while relatively little is transmitted in thefirst order. The desired filtered image appears in the real first order.

As briefly discussed above, this type of filtering or processing systemhas many attendant disadvantages such as high cost and complexity.Additionally, for many applications it is made impractical by itsrequirements, due to the use of coherent light, of very accuratealignment and extreme stability which necessitate an optical bench and askilled. craftsman. Also, the requirement that orders be separatedlimits the size of the image, which in turn limits the size and/orresolution of the object (data) to be filtered. Finally, not only isthere an inefficient use of light in that most of the incident light isdiffracted into the central order, but additionally, real-timeprocessing is precluded due to the requirement that the data to befiltered must be reduced to photographic form such that it can be causedto transmit coherent illumination.

Several attempts have been made in the past to make holographicfiltering more practical. Since all of the above listed problems arisefrom the use of coherent light, attempts have been made to constructincoherent systems. These systems have approximated coherent light byviewing only a small area and have been unsatisfactory due to poorquality.

Most of the above problems are overcome by the novel kinoform filteringtechnique which is the subject of this patent application, In FIG. 2 isillustrated the kinoformic incoherent filtering system. As illustrated,the transparency 9 containing the data to be filtered is illuminated byquasi-monochromatic, temporally incoherent waves 10. The waves 10emanate from, for instance, an incandescent light 1 l and prior to theirarrival atthe object 9 are color filtered by filter 12, such that onlywaves of the spectrum for which the kinoform filter 16 was designed arepassed. The waves are also passed through a diffuser 13. t

The object 9 can be thought of being made up of many point sources, witheach point source of a specified intensity and with a phase varying withtime, i.e., temporally incoherent. The points 14 and 15 represent twosuch point sources. Each point source l4, l5 illuminates the kinoform 16which in turn produces a virtual image l7, 18 positioned as shownrelative to the position of the point source and whose intensity is proportional to the intensity of the point source. Stated matheinatically,if Ha,b,z) is the intensity of the point at (a,b,z) of the virtual imagefrom the kinoform produced by a point source of unit intensity at thepoint (0,0,0), then a distribution of sources with intensity ]6(x,y,z)]2 will produce a virtual image whose intensity is l6(x,y,z) I F(a+x,b+y,z) at the point (a,b,z). Since energy (intensities) are accumulativein incoherent light, the total intensity at point (a,b,z) is given bythe equation If a lens 19 is used to image this virtual pattern onto ascreen or other image recording device 20, then the pattern becomesThese two cases can be thought of as correlation or convolutionalfiltered objects. This system has numerous advantages such as it isrelatively low in cost and is not complex requirements of a coherentsystem. Additionally, there is no noise problem from microscopic dustparticles or flaws in the optics since these are averaged out in anincoherent system. Furthermore, real-time processing can be accomplishedsince it is possible to use real-time data. That is, the data to beprocessed can be displayed on a cathode-ray ,tube and the light from theCRT phosphor used as the illumination. Also, since it is a single ordersystem there is no overlapping order problem which limits the size ofthe object to be filtered and therefore very large objects can befiltered using very small filters.

It should be understood in connection with FIG. 2 that the termincoherent light is used in its true sense. That is, while asillustrated in this figure, for purposes of quality, a diffuser andcolor filter are used along with a separate" source of incoherent light,these members are not required. The ordinary ambient light reflectedfrom a piece of paper having the data to be filtered printed on it issufficient. In this type of simple setup the data is viewed through thekinofonn filter and the eye constitutes the lens or assuming that theambient light is great enough, the filtered image is scanned through thefilter.

Further with respect to color filtering, while in good quality systemsthis is desirable, it is not necessary. That is, the kinoform filterswhich have actually been constructed have been tuned for use with redlight. These filters have been satisfactorily used in systems where theonly light is reflected light from normal fluorescent lights and withillumination from a black-white CRT display.

In summary and to tie in the aforereferenced Kinoform technique which isdescribed in patent application Ser. No. 778,525, a discussion of thecalculation and construction of a filter will be provided.

During calculation of the filter, the impulse response function isconsidered to be a three-dimensional array of point apertures. Eachaperture is assigned a value between zero and one, where zero impliesthat no light is transmitted through the aperture, one implies an openaperture, and the values between represent the relative transmittance ofthe apertures. These values are made to correspond to the square root ofF (x,y,z). These values are read into a calculating machine,

usingfor example punched cards, and a plot tape is generated. 7 V

In the calculations, zeros are appended to the f array so that it is avector of n elements. This interpolates the TE (transform) array:

where am, and T(X 1) for .-n/2 j m/2 and for m/2 j n/2-l. I has therange from n/2 t0 (n/Z-l Since the TE array is of period n, it may berepeated as many times as necessary, to provide a filter as large asdesired. The TE array has the form of TE,,,,=A(l/p) e In the generationof the kinoform filter, only the phase m is used; the amplitude AU/p) isassumed to be constant.

The introduction of the phase factor exp [i(a,b)], which simulates theground glass or the point aperture format alleviates the need forconsidering amplitude in the calculation.

The phase m is plotted on a plotter with, for instance, 32

gray levels, such that for a single wavelength the phase ranges in thatit has neither the extreme alignment nor imaging from 0 to 211 over thescale. For two or three wavelengths the 32 gray levels would be spreadover 0 to 41;- or 0 to 611-, respectively. This alternate approach isadvantageous in that fewer edges occur in the resultant kinoform causingless scattered light. The essential point is that the wave retardationat an edge of the profile must be a multiple integer of a wavelength.The plot is then photoreduced to the appropriate size, governed by thewavelength of light used, and the design distance from the data to befiltered to the filter. The photoreduced device is then etched, forexample, with Kodak etch bath EB-3. The etch bath etches the surface ofthe photoreduction in proportion to the darkening of the photographicreduction. The etching of the photoreduction for a kinoform filter mustbe performed with much more care than is required for conventionalbleached holograms. The relief of the emulsion must be such that lightincident upon a region of d =0 will be retarded by one wavelength,compared with the light incident upon a region of =2r. When phasematching is achieved, almost all of the light incident upon the kinoformfilter will be present in the desired impulse response function with nospurious orders.

While the subject invention has been described systemswise with thefilter being photographically produced, due to the noncriticality of therequired light, both the filter and the data could be real-timedisplayed. This could be accomplished with two deformographic storagedisplay tubes, one for displaying the object to be filtered and a secondto display the desired kinoform. The displays could come from a vidiconor a computer to allow real-time filtering.

Additionally, it will be obvious to those skilled in the art that thesubject invention is equally applicable to other than the optical-typeapplications herein described. Thus, for instance, sonic and ultrasonicfilters could be readily implemented. In this event, however, as will beobvious the filter, while being calculated in exactly the same manner asherein described, would be made of different materials, depending on theapplication. Therefore, other techniques such as cutting and milling,rather than bleaching would be employed.

While the invention has been particularly shown and described withreference to several embodiments, it will be understood by those skilledin the art that various changes in form and detail may be made withoutdepartment from the spirit and scope of the invention.

What is claimed is:

1. A method of performing the mathematic convolution between athree-dimensional convolutional operator with only positive values and athree-dimensional function by processing physical incoherent wavesemanating from a physical amplitude distribution with a processingmember to produce a zero difiraction order output at an output planecomprising the steps of:

A. representing said function by a real physical object which whenilluminated by a wave front scatters said wave front according to saidamplitude distribution to provide said physical incoherent waves;

B. discretizing said convolutional operator across a threedimensionalmatrix to obtain a matrix of positive values;

C. constructing said processing member according to the processes formaking a kinoform wherein said discretized convolutional operator isconsidered to be the intensity of the image projected by said kinoform;and

D. illuminating said processing member with said physical incoherentwaves to selectively retard said waves with resultant interference atsaid output plane in the zero diffraction order corresponding to saidconvolution.

2. The method of claim 1 wherein said physical incoherent waves areincoherent light waves such that optical interference occurs at saidoutput plane.

3. The method of claim 2 wherein said processing member is made of amaterial of substantially uniform transmissivity but with selectivelyvaried thickness corresponding to said controlled phase-retarding areas.

4. The method of claim 3 wherein said selectively varied thickness isobtained b calculating the phase distribution required to produce saioperator in optica form at said output plane with the assumption thatsaid physical incoherent light waves are from a point source, plottingsaid calculated phase distribution as amplitude on a multigrey levelplotter, photoreducing said plot and bleaching said photoreduction.

5. The method of claim 4 wherein said physical incoherent light wavesare provided by a cathode-ray tube having displayed thereon said data tobe processed.

1. A method of performing the mathematic convolution between athree-dimensional convolutional operator with only positive values and athree-dimensional function by processing physical incoherent wavesemanating from a physical amplitude distribution with a processingmember to produce a zero diffraction order output at an output planecomprising the steps of: A. representing said function by a realphysical object which when illuminated by a wave front scatters saidwave front according to said amplitude distribution to provide saidphysical incoherent waves; B. discretizing said convolutional operatoracross a threedimensional matrix to obtain a matrix of positive values;C. constructing said processing member according to the processes formaking a kinoform wherein said discretized convolutional operator isconsidered to be the intensity of the image projected by said kinoform;and D. illuminating said processing member with said physical incoherentwaves to selectively retard said waves with resultant interference atsaid output plane in the zero diffraction order corresponding to saidconvolution.
 2. The method of claim 1 wherein said physical incoherentwaves are incoherent light waves such that optical interference occursat said output plane.
 3. The method of claim 2 wherein said processingmember is made of a material of substantially uniform transmissivity butwith selectively varied thickness corresponding to said controlledphase-retarding areas.
 4. The method of claim 3 wherein said selectivelyvaried thickness is obtained by calculating the phase distributionrequired to produce said operator in optical form at said output planewith the assumption that said physical incoherent light waves are from apoint source, plotting said calculated phase distribution as amplitudeon a multigrey level plotter, photoreducing said plot and bleaching saidphotoreduction.
 5. The method of claim 4 wherein said physicalincoherent light waves are provided by a cathode-ray tube havingdisplayed thereon said data to be processed.